Objectives and Relevance to Program Objectives: This recommended award would support a three-year cooperative research project in mathematics between Professor Gerd Faltings, Department of Mathematics, Princeton University, and Professor Gisbert Wuestholz, University of Wuppertal, Federal Republic of Germany. The mathematicians are collaborating in the area of arithmetic algebraic geometry, a subject particularly concerned with the number of solutions of algebraic equations in several variables when the solutions are restricted to a finite field. Topics of joint research are: (1)questions of effectivity for diophantine problems (classical diophantine equations are polynomial equations for which the unknowns are to be rational numbers), (2)the Shafarevich-conjecture for algebraic surfaces, (3)variations of Hodge-structures and periods, and (4)integer points on abelian varieties. These are topics of extreme interest and profundity in mathematics. Professor Faltings has made important contributions to the field of arithmetic algebraic geometry and is internationally acclaimed for his accomplishments. Professor Wuestholz is a world expert in the techniques necessary to obtain effective results in this area of mathematics. The collaboration of these two investigators is expected to be an extremely productive one. The project thus contributes to an important objective of NSF's cooperative science programs with Western Europe, which is to stimulate scientific progress by bringing together scientists from the U.S. and Europe who have similar research interests and who wish to engage in mutually beneficial research cooperation. Funds from this award would support necessary transportation and partial subsistence expenses for the U.S. principal investigator. Merit of Proposal: There is an excellent prospect that this proposed research will lead to a significant contribution to scientific knowledge. The U.S. principal investigator is a highly respected, productive mathematician. The foreign researcher with whom he will cooperate in the project is also an internationally known expert in this field. Previous collaboration between Professors Faltings and Wuestholz has been productive, and the likelihood of additional mutual benefit from a continuation of the joint effort is high. Funding: This award will not duplicate other funding. The principal investigator receives project support from NSF's Division of Mathematical Sciences, Grant No. DMS-8502316. This recommended INT award would fund the addition of an important international dimension to that research project.
